Reliability models such as fault trees, Markov models, or a combination thereof, are used for the graphical representation and the quantitative analysis of system failures.
Fault trees consist of nodes representing component failures and nodes representing functional failures of systems. They are connected by means of logic gates.
Markov models are stochastic models that assume the Markov property. Generally, this assumption enables reasoning and computation with the model that otherwise would not be possible. Markov modeling and analysis techniques offer applications in the time-based probability, reliability and availability analysis. For the graphical representation and quantitative analysis of system failures, a specific type of Markov models, called continuous-time Markov process may be used. The reliability behavior of a system is represented by a directed graph of states of the system. The system will remain in the current state for some random (in particular, exponentially distributed) amount of time and then transition to a different state. As such, Markov models consist of comprehensive representations of possible chains of events, i.e. transitions, within systems, which in the case of reliability and availability analysis correspond to sequences of failures and repair. The Markov model is analyzed in order to determine the amount of time a system is expected to spend in a given state.
Computing the solution of a Markov model is equivalent to computing the solution of a system of ordinary differential equations, which is done by integration.
A Markov analysis consists at least of three major steps: the specification of the states the system can be in; the specification of the rates at which transitions between states take place, and the computation of the solution to the model.
Fault trees can be regarded as specific embodiments of Markov models.
A fault tree for time-based probability, reliability and availability analysis of a system can be converted into an equivalent Markov model. The vice-versa conversion is generally not possible.
Bayesian networks (or belief networks) are a more general representation of the system. They can be used not only to compute the reliability of the system and to perform fault analysis, but also to assist in system diagnostics.
By exploiting the above referenced reliability models of technical systems such as Markov models, fault trees, and/or a combination of fault trees and Markov models containing embedded or separate reliability data, advanced high fidelity diagnostic tools based on Bayesian networks can be developed quickly and at low cost, without requiring an independent development effort. Currently such diagnostic products are typically not delivered on many systems, especially remote systems to which access is not easily gained, such as subsea applications because of the prohibitive cost.
There is thus a need in the art for a system that converts reliability models such as fault trees, Markov models, or a combination of Markov models and fault trees, automatically into the representation called a Bayesian network that enables a more efficient delivery of system diagnostics, allowing early and accurate detection of failures.